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When pristine material surfaces are exposed to air, highly reactive broken bonds can promote the formation of surface oxides with structures and properties differing greatly from bulk. Determination of the oxide structure, however, is often elusive through the use of indirect diffraction methods or techniques that probe only the outer most layer. As a result, surface oxides forming on widely used materials, such as group III-nitrides, have not been unambiguously resolved, even though critical properties can depend sensitively on their presence. In this work, aberration corrected scanning transmission electron microscopy reveals directly, and with depth dependence, the structure of native two--dimensional oxides that form on AlN and GaN surfaces. Through atomic resolution imaging and spectroscopy, we show that the oxide layers are comprised of tetrahedra--octahedra cation--oxygen units, similar to bulk $\theta$--Al$_2$O$_3$ and $\beta$--Ga$_2$O$_3$. By applying density functional theory, we show that the observed structures are more stable than previously proposed surface oxide models. We place the impact of these observations in the context of key III-nitride growth, device issues, and the recent discovery of two-dimnesional nitrides.